Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(305,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.cn (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 305.5 | ||
Character | \(\chi\) | \(=\) | 624.305 |
Dual form | 624.2.cn.f.401.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.19063 | − | 1.25794i | −0.687410 | − | 0.726270i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.36656 | + | 2.36656i | 1.05836 | + | 1.05836i | 0.998188 | + | 0.0601682i | \(0.0191637\pi\) |
0.0601682 | + | 0.998188i | \(0.480836\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.332282 | − | 1.24009i | 0.125591 | − | 0.468711i | −0.874269 | − | 0.485441i | \(-0.838659\pi\) |
0.999860 | + | 0.0167303i | \(0.00532566\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.164807 | + | 2.99547i | −0.0549358 | + | 0.998490i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.52674 | + | 5.69787i | 0.460329 | + | 1.71797i | 0.671929 | + | 0.740615i | \(0.265466\pi\) |
−0.211600 | + | 0.977356i | \(0.567867\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.51077 | + | 0.821290i | −0.973712 | + | 0.227785i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.159288 | − | 5.79467i | 0.0411279 | − | 1.49618i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.04019 | − | 1.80167i | −0.252284 | − | 0.436969i | 0.711870 | − | 0.702311i | \(-0.247848\pi\) |
−0.964154 | + | 0.265342i | \(0.914515\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.34634 | − | 0.360750i | −0.308871 | − | 0.0827618i | 0.101054 | − | 0.994881i | \(-0.467779\pi\) |
−0.409925 | + | 0.912119i | \(0.634445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.95558 | + | 1.05850i | −0.426743 | + | 0.230984i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.81352 | + | 6.60522i | −0.795175 | + | 1.37728i | 0.127553 | + | 0.991832i | \(0.459288\pi\) |
−0.922728 | + | 0.385452i | \(0.874046\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.20118i | 1.24024i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.96433 | − | 3.35917i | 0.762936 | − | 0.646473i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.87044 | + | 3.96665i | 1.27581 | + | 0.736588i | 0.976075 | − | 0.217435i | \(-0.0697689\pi\) |
0.299733 | + | 0.954023i | \(0.403102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.42567 | + | 1.42567i | −0.256058 | + | 0.256058i | −0.823449 | − | 0.567391i | \(-0.807953\pi\) |
0.567391 | + | 0.823449i | \(0.307953\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.34977 | − | 8.70458i | 0.931276 | − | 1.51527i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.72111 | − | 2.14839i | 0.628983 | − | 0.363143i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.28784 | − | 1.14892i | 0.704917 | − | 0.188882i | 0.111485 | − | 0.993766i | \(-0.464439\pi\) |
0.593432 | + | 0.804884i | \(0.297773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.21315 | + | 3.43847i | 0.834772 | + | 0.550596i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.985195 | + | 0.263982i | −0.153862 | + | 0.0412271i | −0.334928 | − | 0.942244i | \(-0.608712\pi\) |
0.181066 | + | 0.983471i | \(0.442045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.68002 | − | 5.01141i | 1.32369 | − | 0.764233i | 0.339376 | − | 0.940651i | \(-0.389784\pi\) |
0.984315 | + | 0.176418i | \(0.0564509\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.47898 | + | 6.69892i | −1.11490 | + | 0.998617i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.59357 | + | 2.59357i | −0.378312 | + | 0.378312i | −0.870493 | − | 0.492181i | \(-0.836200\pi\) |
0.492181 | + | 0.870493i | \(0.336200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.63476 | + | 2.67588i | 0.662109 | + | 0.382269i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.02790 | + | 3.45361i | −0.143935 | + | 0.483603i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.08357i | − | 0.973003i | −0.873680 | − | 0.486501i | \(-0.838273\pi\) | ||
0.873680 | − | 0.486501i | \(-0.161727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.87121 | + | 17.0974i | −1.33103 | + | 2.30542i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.14919 | + | 2.12313i | 0.152214 | + | 0.281215i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.48170 | − | 0.397021i | −0.192901 | − | 0.0516877i | 0.161075 | − | 0.986942i | \(-0.448504\pi\) |
−0.353976 | + | 0.935254i | \(0.615171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.39878 | + | 5.88685i | 0.435169 | + | 0.753734i | 0.997309 | − | 0.0733074i | \(-0.0233554\pi\) |
−0.562141 | + | 0.827042i | \(0.690022\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.65990 | + | 1.19972i | 0.461104 | + | 0.151150i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.2521 | − | 6.36480i | −1.27161 | − | 0.789456i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.22473 | + | 8.30282i | 0.271794 | + | 1.01435i | 0.957959 | + | 0.286904i | \(0.0926262\pi\) |
−0.686165 | + | 0.727446i | \(0.740707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.8494 | − | 3.06719i | 1.54689 | − | 0.369246i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.21596 | − | 4.53804i | 0.144308 | − | 0.538566i | −0.855477 | − | 0.517841i | \(-0.826736\pi\) |
0.999785 | − | 0.0207249i | \(-0.00659741\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.61981 | − | 9.61981i | −1.12591 | − | 1.12591i | −0.990835 | − | 0.135079i | \(-0.956871\pi\) |
−0.135079 | − | 0.990835i | \(-0.543129\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.80069 | − | 7.38331i | 0.900746 | − | 0.852551i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.57319 | 0.863045 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7272 | 1.31941 | 0.659706 | − | 0.751524i | \(-0.270681\pi\) | ||||
0.659706 | + | 0.751524i | \(0.270681\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.94568 | − | 0.987351i | −0.993964 | − | 0.109706i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.406364 | + | 0.406364i | 0.0446042 | + | 0.0446042i | 0.729057 | − | 0.684453i | \(-0.239959\pi\) |
−0.684453 | + | 0.729057i | \(0.739959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.80207 | − | 6.72543i | 0.195462 | − | 0.729475i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.19035 | − | 13.3654i | −0.342041 | − | 1.43292i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.75705 | − | 6.55739i | −0.186247 | − | 0.695081i | −0.994360 | − | 0.106055i | \(-0.966178\pi\) |
0.808114 | − | 0.589026i | \(-0.200489\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.148089 | + | 4.62658i | −0.0155239 | + | 0.484997i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.49085 | + | 0.0959586i | 0.361984 | + | 0.00995045i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.33245 | − | 4.03992i | −0.239304 | − | 0.414487i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.89119 | − | 1.57854i | −0.598160 | − | 0.160276i | −0.0529800 | − | 0.998596i | \(-0.516872\pi\) |
−0.545180 | + | 0.838319i | \(0.683539\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.3194 | + | 3.63425i | −1.74067 | + | 0.365256i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.42569 | + | 9.39757i | −0.539876 | + | 0.935093i | 0.459034 | + | 0.888419i | \(0.348196\pi\) |
−0.998910 | + | 0.0466743i | \(0.985138\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.53207i | − | 0.545091i | −0.962143 | − | 0.272546i | \(-0.912134\pi\) | ||
0.962143 | − | 0.272546i | \(-0.0878656\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.13300 | − | 2.12299i | −0.696109 | − | 0.207183i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.21782 | + | 2.43516i | 0.407752 | + | 0.235416i | 0.689823 | − | 0.723978i | \(-0.257688\pi\) |
−0.282071 | + | 0.959393i | \(0.591022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.33269 | − | 1.33269i | 0.127649 | − | 0.127649i | −0.640396 | − | 0.768045i | \(-0.721230\pi\) |
0.768045 | + | 0.640396i | \(0.221230\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.55050 | − | 4.02589i | −0.621746 | − | 0.382121i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.42921 | − | 4.86661i | 0.792954 | − | 0.457812i | −0.0480476 | − | 0.998845i | \(-0.515300\pi\) |
0.841001 | + | 0.541033i | \(0.181967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.6565 | + | 6.60670i | −2.29924 | + | 0.616078i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.88155 | − | 10.6517i | −0.173949 | − | 0.984755i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.57987 | + | 0.691275i | −0.236496 | + | 0.0633690i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.6085 | + | 11.8983i | −1.87350 | + | 1.08166i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.50507 | + | 0.925008i | 0.135708 | + | 0.0834052i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.84267 | + | 2.84267i | −0.254256 | + | 0.254256i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.90233 | − | 2.25301i | −0.346276 | − | 0.199923i | 0.316768 | − | 0.948503i | \(-0.397402\pi\) |
−0.663044 | + | 0.748581i | \(0.730736\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.6387 | − | 4.95218i | −1.46496 | − | 0.436015i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.24622i | − | 0.545735i | −0.962052 | − | 0.272867i | \(-0.912028\pi\) | ||
0.962052 | − | 0.272867i | \(-0.0879721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.894727 | + | 1.54971i | −0.0775827 | + | 0.134377i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.3315 | + | 1.43214i | 1.49166 | + | 0.123259i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.2503 | − | 5.96195i | −1.90097 | − | 0.509364i | −0.996577 | − | 0.0826685i | \(-0.973656\pi\) |
−0.904395 | − | 0.426696i | \(-0.859678\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.56760 | − | 16.5716i | −0.811513 | − | 1.40558i | −0.911805 | − | 0.410624i | \(-0.865311\pi\) |
0.100292 | − | 0.994958i | \(-0.468022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.35053 | + | 0.174568i | 0.534811 | + | 0.0147012i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0396 | − | 18.7500i | −0.839556 | − | 1.56795i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.87198 | + | 25.6466i | 0.570687 | + | 2.12983i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.15219 | − | 9.01621i | −0.177510 | − | 0.743645i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.46420 | − | 12.9286i | 0.283798 | − | 1.05915i | −0.665915 | − | 0.746028i | \(-0.731958\pi\) |
0.949713 | − | 0.313122i | \(-0.101375\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.77938 | + | 8.77938i | 0.714455 | + | 0.714455i | 0.967464 | − | 0.253009i | \(-0.0814201\pi\) |
−0.253009 | + | 0.967464i | \(0.581420\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.56827 | − | 2.81894i | 0.450168 | − | 0.227898i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.74786 | −0.542001 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.27714 | 0.261544 | 0.130772 | − | 0.991412i | \(-0.458254\pi\) | ||||
0.130772 | + | 0.991412i | \(0.458254\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.91068 | + | 8.43390i | −0.706663 | + | 0.668852i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92392 | + | 6.92392i | 0.545681 | + | 0.545681i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.17349 | − | 4.37951i | 0.0919145 | − | 0.343030i | −0.904619 | − | 0.426221i | \(-0.859845\pi\) |
0.996534 | + | 0.0831914i | \(0.0265113\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 33.2604 | − | 7.93935i | 2.58932 | − | 0.618077i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.16836 | − | 8.09242i | −0.167793 | − | 0.626210i | −0.997668 | − | 0.0682609i | \(-0.978255\pi\) |
0.829875 | − | 0.557949i | \(-0.188412\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6510 | − | 5.76671i | 0.896228 | − | 0.443593i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.30250 | − | 3.97346i | 0.0996049 | − | 0.303858i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.39731 | + | 12.8125i | 0.562407 | + | 0.974118i | 0.997286 | + | 0.0736289i | \(0.0234580\pi\) |
−0.434878 | + | 0.900489i | \(0.643209\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.69004 | + | 2.06054i | 0.581312 | + | 0.155762i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.26473 | + | 2.33659i | 0.0950629 | + | 0.175629i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.299519 | − | 0.518782i | 0.0223871 | − | 0.0387756i | −0.854615 | − | 0.519262i | \(-0.826207\pi\) |
0.877002 | + | 0.480487i | \(0.159540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.8056i | 1.24915i | 0.780964 | + | 0.624576i | \(0.214728\pi\) | ||||
−0.780964 | + | 0.624576i | \(0.785272\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.35861 | − | 11.2845i | 0.248275 | − | 0.834174i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.8664 | + | 7.42843i | 0.945958 | + | 0.546149i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.67756 | − | 8.67756i | 0.634566 | − | 0.634566i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.84841 | − | 6.03233i | −0.207191 | − | 0.438788i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.19095 | − | 2.41964i | 0.303246 | − | 0.175079i | −0.340654 | − | 0.940189i | \(-0.610648\pi\) |
0.643900 | + | 0.765109i | \(0.277315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.47201 | − | 2.27007i | 0.609828 | − | 0.163403i | 0.0593289 | − | 0.998238i | \(-0.481104\pi\) |
0.550500 | + | 0.834835i | \(0.314437\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.19988 | + | 20.4745i | 0.300760 | + | 1.46621i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8579 | + | 5.32092i | −1.41482 | + | 0.379100i | −0.883643 | − | 0.468162i | \(-0.844916\pi\) |
−0.531176 | + | 0.847261i | \(0.678250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.29567 | + | 0.748053i | −0.0918473 | + | 0.0530281i | −0.545220 | − | 0.838293i | \(-0.683554\pi\) |
0.453373 | + | 0.891321i | \(0.350221\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.79558 | − | 12.6841i | 0.549858 | − | 0.894670i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.20193 | − | 7.20193i | 0.505477 | − | 0.505477i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.95625 | − | 1.70679i | −0.206473 | − | 0.119208i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.1572 | − | 12.5119i | −1.33152 | − | 0.869636i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.22203i | − | 0.568729i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.74572 | − | 13.4160i | 0.533237 | − | 0.923594i | −0.466009 | − | 0.884780i | \(-0.654309\pi\) |
0.999246 | − | 0.0388139i | \(-0.0123579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.15632 | + | 3.87351i | −0.490343 | + | 0.265409i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.4016 | + | 8.68197i | 2.20977 | + | 0.592106i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.29424 | + | 2.24169i | 0.0878587 | + | 0.152176i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.647487 | + | 23.5547i | −0.0437531 | + | 1.59168i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.13157 | + | 5.47093i | 0.345187 | + | 0.368015i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.86321 | + | 18.1498i | 0.325665 | + | 1.21540i | 0.913642 | + | 0.406520i | \(0.133258\pi\) |
−0.587977 | + | 0.808878i | \(0.700075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.5755 | − | 1.02200i | −1.23836 | − | 0.0681334i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.273750 | + | 1.02165i | −0.0181694 | + | 0.0678093i | −0.974415 | − | 0.224755i | \(-0.927842\pi\) |
0.956246 | + | 0.292564i | \(0.0945085\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.97504 | + | 5.97504i | 0.394842 | + | 0.394842i | 0.876409 | − | 0.481567i | \(-0.159932\pi\) |
−0.481567 | + | 0.876409i | \(0.659932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.01686 | − | 9.52659i | −0.593266 | − | 0.626804i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.30436 | −0.150964 | −0.0754820 | − | 0.997147i | \(-0.524050\pi\) | ||||
−0.0754820 | + | 0.997147i | \(0.524050\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.2757 | −0.800777 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.9627 | − | 14.7521i | −0.906977 | − | 0.958249i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.0131657 | − | 0.0131657i | −0.000851621 | − | 0.000851621i | 0.706681 | − | 0.707532i | \(-0.250192\pi\) |
−0.707532 | + | 0.706681i | \(0.750192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.35079 | − | 16.2374i | 0.280259 | − | 1.04594i | −0.671976 | − | 0.740573i | \(-0.734554\pi\) |
0.952235 | − | 0.305367i | \(-0.0987792\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.40895 | + | 12.4287i | 0.603585 | + | 0.797299i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.63580 | + | 17.3010i | 0.296170 | + | 1.10532i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.02296 | + | 0.160776i | 0.319603 | + | 0.0102299i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0273514 | − | 0.995008i | 0.00173333 | − | 0.0630561i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.88393 | + | 11.9233i | 0.434510 | + | 0.752593i | 0.997255 | − | 0.0740371i | \(-0.0235883\pi\) |
−0.562746 | + | 0.826630i | \(0.690255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −43.4579 | − | 11.6445i | −2.73218 | − | 0.732084i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.6058 | + | 5.74059i | −0.664158 | + | 0.359490i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.82331 | − | 10.0863i | 0.363248 | − | 0.629164i | −0.625245 | − | 0.780428i | \(-0.715001\pi\) |
0.988493 | + | 0.151264i | \(0.0483344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.69909i | − | 0.354124i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.0143 | + | 19.9265i | −0.805563 | + | 1.23342i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.2887 | + | 12.2910i | 1.31271 | + | 0.757896i | 0.982545 | − | 0.186025i | \(-0.0595606\pi\) |
0.330170 | + | 0.943922i | \(0.392894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.7637 | − | 16.7637i | 1.02978 | − | 1.02978i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.15678 | + | 10.0177i | −0.376789 | + | 0.613071i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.83996 | − | 1.06230i | 0.112184 | − | 0.0647697i | −0.442858 | − | 0.896592i | \(-0.646035\pi\) |
0.555042 | + | 0.831822i | \(0.312702\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.53449 | + | 0.679116i | −0.153960 | + | 0.0412533i | −0.334976 | − | 0.942227i | \(-0.608728\pi\) |
0.181016 | + | 0.983480i | \(0.442061\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.99626 | − | 5.32225i | 0.362910 | − | 0.322117i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −35.3335 | + | 9.46759i | −2.13069 | + | 0.570917i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.6137 | − | 10.1693i | 1.05831 | − | 0.611013i | 0.133342 | − | 0.991070i | \(-0.457429\pi\) |
0.924963 | + | 0.380057i | \(0.124096\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.03559 | − | 4.50551i | −0.241605 | − | 0.269738i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.9749 | + | 21.9749i | −1.31091 | + | 1.31091i | −0.390172 | + | 0.920742i | \(0.627585\pi\) |
−0.920742 | + | 0.390172i | \(0.872415\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.14892 | + | 1.24068i | 0.127740 | + | 0.0737508i | 0.562508 | − | 0.826792i | \(-0.309836\pi\) |
−0.434768 | + | 0.900542i | \(0.643170\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.30488 | + | 7.74412i | −0.136529 | + | 0.458722i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.30945i | 0.0772944i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.33600 | − | 10.9743i | 0.372706 | − | 0.645545i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.02852 | + | 9.29020i | 0.294777 | + | 0.544601i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.05925 | + | 1.62357i | 0.353985 | + | 0.0948500i | 0.431429 | − | 0.902147i | \(-0.358009\pi\) |
−0.0774445 | + | 0.996997i | \(0.524676\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.56696 | − | 4.44610i | −0.149454 | − | 0.258862i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.1926 | + | 17.4597i | 1.46182 | + | 1.01311i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.96360 | − | 26.3214i | 0.460547 | − | 1.52221i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.33040 | − | 12.4292i | −0.191961 | − | 0.716409i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.2815 | − | 4.36384i | 1.05025 | − | 0.250696i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.88817 | + | 21.9750i | −0.337156 | + | 1.25828i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.38970 | + | 3.38970i | 0.193461 | + | 0.193461i | 0.797190 | − | 0.603729i | \(-0.206319\pi\) |
−0.603729 | + | 0.797190i | \(0.706319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.95899 | + | 6.58664i | −0.395883 | + | 0.374701i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.8546 | −1.18255 | −0.591277 | − | 0.806469i | \(-0.701376\pi\) | ||||
−0.591277 | + | 0.806469i | \(0.701376\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0202 | −1.24465 | −0.622327 | − | 0.782757i | \(-0.713813\pi\) | ||||
−0.622327 | + | 0.782757i | \(0.713813\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.82216 | + | 11.5006i | 0.328041 | + | 0.647983i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4092 | + | 12.4092i | 0.696968 | + | 0.696968i | 0.963755 | − | 0.266787i | \(-0.0859621\pi\) |
−0.266787 | + | 0.963755i | \(0.585962\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.1121 | + | 45.2029i | −0.678146 | + | 2.53088i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.95858 | − | 8.20512i | −0.109317 | − | 0.457965i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.750500 | + | 2.80090i | 0.0417589 | + | 0.155846i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.09297 | − | 21.7709i | −0.282507 | − | 1.20763i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.26318 | − | 0.0897003i | −0.180454 | − | 0.00496044i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.35447 | + | 4.07807i | 0.129806 | + | 0.224831i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.7039 | − | 2.86810i | −0.588340 | − | 0.157645i | −0.0476456 | − | 0.998864i | \(-0.515172\pi\) |
−0.540694 | + | 0.841219i | \(0.681838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.73490 | + | 13.0334i | 0.149871 | + | 0.714229i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.3841 | + | 24.9140i | −0.785889 | + | 1.36120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.4976i | − | 0.735259i | −0.929972 | − | 0.367630i | \(-0.880169\pi\) | ||
0.929972 | − | 0.367630i | \(-0.119831\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.1579 | − | 4.80909i | −0.877579 | − | 0.261194i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2999 | − | 5.94666i | −0.557771 | − | 0.322029i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.2131 | − | 11.2131i | 0.605448 | − | 0.605448i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 37.6676 | + | 23.1502i | 2.02796 | + | 1.24637i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.61214 | − | 5.54957i | 0.516007 | − | 0.297917i | −0.219293 | − | 0.975659i | \(-0.570375\pi\) |
0.735299 | + | 0.677742i | \(0.237042\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.6033 | − | 5.52063i | 1.10287 | − | 0.295512i | 0.338936 | − | 0.940810i | \(-0.389933\pi\) |
0.763932 | + | 0.645297i | \(0.223266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.1590 | + | 15.0491i | −0.595623 | + | 0.803264i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.4311 | − | 4.67065i | 0.927765 | − | 0.248594i | 0.236863 | − | 0.971543i | \(-0.423881\pi\) |
0.690901 | + | 0.722949i | \(0.257214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.6172 | − | 7.86187i | 0.722724 | − | 0.417265i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.94125 | + | 2.42226i | 0.208593 | + | 0.128200i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.6950 | − | 10.6950i | 0.564462 | − | 0.564462i | −0.366110 | − | 0.930572i | \(-0.619311\pi\) |
0.930572 | + | 0.366110i | \(0.119311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7720 | − | 8.52862i | −0.777474 | − | 0.448875i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 39.5044 | + | 11.7577i | 2.07344 | + | 0.617118i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 45.5317i | − | 2.38324i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.7893 | − | 25.6158i | 0.771995 | − | 1.33713i | −0.164473 | − | 0.986382i | \(-0.552592\pi\) |
0.936468 | − | 0.350753i | \(-0.114074\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.628384 | − | 2.99463i | −0.0327123 | − | 0.155894i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.78428 | − | 2.35374i | −0.456057 | − | 0.122200i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.76737 | + | 16.9176i | 0.505735 | + | 0.875959i | 0.999978 | + | 0.00663494i | \(0.00211198\pi\) |
−0.494243 | + | 0.869324i | \(0.664555\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.96046 | + | 0.191334i | 0.359437 | + | 0.00988042i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.3783 | − | 8.28336i | −1.41005 | − | 0.426615i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.69053 | − | 32.4335i | −0.446402 | − | 1.66600i | −0.712207 | − | 0.701970i | \(-0.752304\pi\) |
0.265804 | − | 0.964027i | \(-0.414363\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.81208 | + | 7.59139i | 0.0928358 | + | 0.388919i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.45165 | − | 5.41763i | 0.0741758 | − | 0.276828i | −0.918869 | − | 0.394562i | \(-0.870896\pi\) |
0.993045 | + | 0.117734i | \(0.0375630\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.9224 | + | 17.9224i | 0.913409 | + | 0.913409i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.5810 | + | 26.8267i | 0.690361 | + | 1.36368i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1875 | −0.719336 | −0.359668 | − | 0.933080i | \(-0.617110\pi\) | ||||
−0.359668 | + | 0.933080i | \(0.617110\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8672 | 0.802439 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.85735 | + | 7.43693i | −0.396351 | + | 0.375144i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.7531 | + | 27.7531i | 1.39641 | + | 1.39641i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0364 | + | 37.4565i | −0.503714 | + | 1.87989i | −0.0293274 | + | 0.999570i | \(0.509337\pi\) |
−0.474387 | + | 0.880317i | \(0.657330\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.01473 | − | 0.719623i | 0.150925 | − | 0.0360262i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.47565 | − | 9.23926i | −0.123628 | − | 0.461387i | 0.876159 | − | 0.482022i | \(-0.160098\pi\) |
−0.999787 | + | 0.0206358i | \(0.993431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.83431 | − | 6.17609i | 0.191001 | − | 0.307653i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.8338 | − | 23.5071i | −0.935861 | − | 1.16808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.0928 | + | 22.6774i | 0.648987 | + | 1.12408i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.7151 | + | 7.96215i | 1.46932 | + | 0.393703i | 0.902698 | − | 0.430275i | \(-0.141583\pi\) |
0.566622 | + | 0.823978i | \(0.308250\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.9921 | + | 35.0879i | 0.936811 | + | 1.73076i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.984685 | + | 1.70552i | −0.0484532 | + | 0.0839234i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.92337i | 0.0944143i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.45452 | + | 31.7660i | −0.462990 | + | 1.55559i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.1024 | − | 17.3796i | −1.47060 | − | 0.849051i | −0.471145 | − | 0.882056i | \(-0.656159\pi\) |
−0.999455 | + | 0.0330044i | \(0.989492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.85119 | + | 2.85119i | −0.138959 | + | 0.138959i | −0.773164 | − | 0.634206i | \(-0.781327\pi\) |
0.634206 | + | 0.773164i | \(0.281327\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.34153 | − | 8.19641i | −0.356957 | − | 0.398523i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.1725 | − | 6.45043i | 0.541944 | − | 0.312892i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.42959 | − | 2.25870i | 0.407937 | − | 0.109306i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.6328 | + | 34.9535i | −0.561638 | + | 1.68757i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0403 | + | 3.49414i | −0.628129 | + | 0.168307i | −0.558820 | − | 0.829289i | \(-0.688746\pi\) |
−0.0693083 | + | 0.997595i | \(0.522079\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.21603 | + | 4.16618i | −0.346781 | + | 0.200214i | −0.663266 | − | 0.748383i | \(-0.730830\pi\) |
0.316486 | + | 0.948597i | \(0.397497\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.0798 | − | 39.1801i | 1.15454 | − | 1.87854i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.51713 | − | 7.51713i | 0.359593 | − | 0.359593i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.5522 | − | 10.7111i | −0.885447 | − | 0.511213i | −0.0129962 | − | 0.999916i | \(-0.504137\pi\) |
−0.872450 | + | 0.488703i | \(0.837470\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.77936 | + | 13.4423i | −0.418065 | + | 0.640108i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.8889i | − | 0.564859i | −0.959288 | − | 0.282430i | \(-0.908860\pi\) | ||
0.959288 | − | 0.282430i | \(-0.0911404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.3603 | − | 19.6766i | 0.538529 | − | 0.932759i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.3879 | + | 11.0354i | −0.964315 | + | 0.521956i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.5028 | + | 7.63730i | 1.34513 | + | 0.360427i | 0.858335 | − | 0.513089i | \(-0.171499\pi\) |
0.486795 | + | 0.873516i | \(0.338166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.00827 | − | 5.21048i | −0.141654 | − | 0.245352i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.590920 | − | 21.4969i | 0.0277638 | − | 1.01001i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.2995 | + | 10.5986i | −0.529729 | + | 0.496870i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.778148 | + | 2.90409i | 0.0364002 | + | 0.135848i | 0.981735 | − | 0.190255i | \(-0.0609313\pi\) |
−0.945335 | + | 0.326102i | \(0.894265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.1758 | − | 3.64822i | −0.474965 | − | 0.170284i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.56519 | − | 24.5016i | 0.305771 | − | 1.14115i | −0.626508 | − | 0.779415i | \(-0.715516\pi\) |
0.932279 | − | 0.361739i | \(-0.117817\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.1905 | − | 24.1905i | −1.12423 | − | 1.12423i | −0.991098 | − | 0.133132i | \(-0.957497\pi\) |
−0.133132 | − | 0.991098i | \(-0.542503\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.03420 | + | 8.48838i | 0.372577 | + | 0.393639i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.4165 | −1.54633 | −0.773166 | − | 0.634204i | \(-0.781328\pi\) | ||||
−0.773166 | + | 0.634204i | \(0.781328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0355 | 0.509572 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.90185 | − | 4.12243i | −0.179788 | − | 0.189952i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 41.8065 | + | 41.8065i | 1.92226 | + | 1.92226i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.23708 | − | 8.34889i | 0.102644 | − | 0.383073i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.2186 | + | 1.16742i | 0.971534 | + | 0.0534527i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.90851 | + | 18.3188i | 0.224275 | + | 0.837007i | 0.982693 | + | 0.185239i | \(0.0593059\pi\) |
−0.758418 | + | 0.651768i | \(0.774027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.1100 | + | 7.55516i | −0.643361 | + | 0.344486i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.466033 | − | 16.9537i | 0.0212052 | − | 0.771418i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.2061 | − | 17.6775i | −0.463437 | − | 0.802696i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.74563 | + | 0.467740i | 0.0791021 | + | 0.0211953i | 0.298153 | − | 0.954518i | \(-0.403629\pi\) |
−0.219051 | + | 0.975713i | \(0.570296\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.90633 | + | 3.73820i | −0.312315 | + | 0.169047i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.52793 | + | 11.3067i | −0.294601 | + | 0.510265i | −0.974892 | − | 0.222678i | \(-0.928520\pi\) |
0.680291 | + | 0.732942i | \(0.261854\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16.5043i | − | 0.743317i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −49.5880 | − | 32.3867i | −2.22882 | − | 1.45567i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.22354 | − | 3.01581i | −0.234308 | − | 0.135278i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.7768 | − | 10.7768i | 0.482436 | − | 0.482436i | −0.423473 | − | 0.905909i | \(-0.639189\pi\) |
0.905909 | + | 0.423473i | \(0.139189\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.59804 | + | 12.3627i | −0.339455 | + | 0.552326i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.3942 | − | 21.5895i | 1.66732 | − | 0.962630i | 0.698251 | − | 0.715853i | \(-0.253962\pi\) |
0.969072 | − | 0.246777i | \(-0.0793714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.0801 | + | 9.39968i | −1.56104 | + | 0.418280i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.1261 | − | 7.79016i | −0.938244 | − | 0.345973i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.6268 | + | 2.84743i | −0.471023 | + | 0.126210i | −0.486520 | − | 0.873670i | \(-0.661734\pi\) |
0.0154964 | + | 0.999880i | \(0.495067\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.1259 | + | 8.73297i | −0.669132 | + | 0.386324i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.54916 | + | 3.09245i | −0.289152 | + | 0.136535i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.0920 | − | 13.0920i | 0.576901 | − | 0.576901i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.7375 | − | 10.8181i | −0.824076 | − | 0.475781i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.30989 | − | 24.5603i | 0.320868 | − | 1.07808i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.17222i | − | 0.270410i | −0.990818 | − | 0.135205i | \(-0.956831\pi\) | ||
0.990818 | − | 0.135205i | \(-0.0431692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.876655 | − | 1.51841i | 0.0383334 | − | 0.0663954i | −0.846222 | − | 0.532830i | \(-0.821128\pi\) |
0.884556 | + | 0.466435i | \(0.154462\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.56395 | − | 12.1269i | −0.286474 | − | 0.529262i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.05156 | + | 1.08561i | 0.176489 | + | 0.0472900i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5859 | − | 30.4597i | −0.764606 | − | 1.32434i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.43346 | − | 4.37296i | 0.0622068 | − | 0.189770i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.24199 | − | 1.73591i | 0.140426 | − | 0.0751907i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.21877 | + | 15.7446i | 0.182393 | + | 0.680701i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.00921 | + | 0.240901i | −0.0435506 | + | 0.0103956i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.17074 | + | 30.4936i | −0.351939 | + | 1.31345i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8540 | + | 13.8540i | 0.595630 | + | 0.595630i | 0.939147 | − | 0.343517i | \(-0.111618\pi\) |
−0.343517 | + | 0.939147i | \(0.611618\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.1404 | − | 20.0092i | 0.907221 | − | 0.858679i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.30777 | 0.270195 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.1018 | 0.560192 | 0.280096 | − | 0.959972i | \(-0.409634\pi\) | ||||
0.280096 | + | 0.959972i | \(0.409634\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.1940 | + | 9.21073i | −0.776502 | + | 0.393104i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.81896 | − | 7.81896i | −0.333099 | − | 0.333099i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.89673 | − | 14.5428i | 0.165706 | − | 0.618423i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.97463 | − | 25.0296i | −0.253609 | − | 1.06245i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.48270 | + | 12.9976i | 0.147567 | + | 0.550726i | 0.999628 | + | 0.0272837i | \(0.00868574\pi\) |
−0.852061 | + | 0.523442i | \(0.824648\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.3577 | + | 24.7227i | −1.11481 | + | 1.04566i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.2476 | − | 0.584067i | −0.897073 | − | 0.0246593i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.92896 | + | 3.34105i | 0.0812959 | + | 0.140809i | 0.903807 | − | 0.427941i | \(-0.140761\pi\) |
−0.822511 | + | 0.568749i | \(0.807427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.4653 | + | 8.43111i | 1.32376 | + | 0.354699i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.19689 | + | 10.7654i | −0.176253 | + | 0.452104i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.1796 | − | 36.6841i | 0.887895 | − | 1.53788i | 0.0455351 | − | 0.998963i | \(-0.485501\pi\) |
0.842360 | − | 0.538916i | \(-0.181166\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5465i | 0.734300i | 0.930162 | + | 0.367150i | \(0.119666\pi\) | ||||
−0.930162 | + | 0.367150i | \(0.880334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.03362 | − | 2.39105i | −0.335609 | − | 0.0998874i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −40.9602 | − | 23.6484i | −1.70816 | − | 0.986205i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.37810 | + | 7.37810i | −0.307154 | + | 0.307154i | −0.843805 | − | 0.536650i | \(-0.819689\pi\) |
0.536650 | + | 0.843805i | \(0.319689\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.9426 | − | 7.95444i | −0.537877 | − | 0.330575i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.638956 | − | 0.368901i | 0.0265084 | − | 0.0153046i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.3612 | − | 10.8148i | 1.67159 | − | 0.447902i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20.7552 | − | 29.6608i | 0.858121 | − | 1.22632i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.4131 | − | 8.41711i | 1.29656 | − | 0.347411i | 0.456410 | − | 0.889770i | \(-0.349135\pi\) |
0.840147 | + | 0.542358i | \(0.182468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.43375 | − | 1.40512i | 0.100281 | − | 0.0578971i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.3368 | + | 18.6448i | 1.24789 | + | 0.766944i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.50934 | − | 2.50934i | 0.103046 | − | 0.103046i | −0.653704 | − | 0.756750i | \(-0.726786\pi\) |
0.756750 | + | 0.653704i | \(0.226786\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.74135 | − | 4.46947i | −0.317365 | − | 0.183231i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.48366 | + | 0.739212i | 0.101649 | + | 0.0302539i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.2005i | 1.02967i | 0.857291 | + | 0.514833i | \(0.172146\pi\) | ||||
−0.857291 | + | 0.514833i | \(0.827854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.3583 | − | 17.9411i | 0.422525 | − | 0.731834i | −0.573661 | − | 0.819093i | \(-0.694477\pi\) |
0.996186 | + | 0.0872588i | \(0.0278107\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.2375 | + | 5.29575i | −1.02775 | + | 0.215660i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −76.9292 | − | 20.6131i | −3.12762 | − | 0.838042i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.69471 | + | 4.66737i | 0.109375 | + | 0.189443i | 0.915517 | − | 0.402279i | \(-0.131782\pi\) |
−0.806142 | + | 0.591722i | \(0.798448\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.6344 | − | 0.484746i | −0.714582 | − | 0.0196429i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.97536 | − | 11.2355i | 0.282193 | − | 0.454540i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.44016 | + | 16.5709i | 0.179336 | + | 0.669292i | 0.995772 | + | 0.0918561i | \(0.0292800\pi\) |
−0.816436 | + | 0.577436i | \(0.804053\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.37276 | + | 5.75093i | 0.0553550 | + | 0.231900i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.71774 | − | 13.8748i | 0.149671 | − | 0.558579i | −0.849832 | − | 0.527053i | \(-0.823297\pi\) |
0.999503 | − | 0.0315255i | \(-0.0100365\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.5212 | + | 26.5212i | 1.06598 | + | 1.06598i | 0.997664 | + | 0.0683140i | \(0.0217620\pi\) |
0.0683140 | + | 0.997664i | \(0.478238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.07000 | + | 38.9956i | 0.283709 | + | 1.56484i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.71560 | −0.349183 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.5512 | 0.702050 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.3428 | + | 9.78938i | −0.413051 | + | 0.390950i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.53016 | − | 6.53016i | −0.260375 | − | 0.260375i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.01788 | − | 11.2629i | 0.120140 | − | 0.448369i | −0.879480 | − | 0.475936i | \(-0.842109\pi\) |
0.999620 | + | 0.0275672i | \(0.00877604\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.0987 | + | 6.22982i | −1.03733 | + | 0.247613i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.90321 | − | 14.5670i | −0.154894 | − | 0.578073i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.4692 | − | 5.58791i | −0.731778 | − | 0.221401i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.3932 | + | 4.39028i | 0.529825 | + | 0.173677i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.6100 | + | 21.8411i | 0.498063 | + | 0.862671i | 0.999998 | − | 0.00223486i | \(-0.000711379\pi\) |
−0.501934 | + | 0.864906i | \(0.667378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.7951 | − | 10.6631i | −1.56937 | − | 0.420511i | −0.633753 | − | 0.773535i | \(-0.718486\pi\) |
−0.935614 | + | 0.353025i | \(0.885153\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.6569 | − | 51.0961i | −1.08899 | − | 2.01191i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.88978 | − | 5.00524i | 0.113609 | − | 0.196776i | −0.803614 | − | 0.595151i | \(-0.797092\pi\) |
0.917223 | + | 0.398375i | \(0.130426\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.04868i | − | 0.355192i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.27894 | − | 4.29709i | 0.0501257 | − | 0.168416i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.36540 | + | 3.09771i | 0.209964 | + | 0.121223i | 0.601295 | − | 0.799027i | \(-0.294652\pi\) |
−0.391330 | + | 0.920250i | \(0.627985\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.7820 | − | 14.7820i | 0.577582 | − | 0.577582i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.4013 | − | 27.2304i | 1.18607 | − | 1.06236i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.8116 | + | 10.2836i | −0.693843 | + | 0.400590i | −0.805050 | − | 0.593207i | \(-0.797862\pi\) |
0.111207 | + | 0.993797i | \(0.464528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.1745 | + | 11.0327i | −1.60150 | + | 0.429121i | −0.945496 | − | 0.325634i | \(-0.894422\pi\) |
−0.656007 | + | 0.754755i | \(0.727756\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.772297 | − | 12.9690i | 0.0299935 | − | 0.503676i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.78491 | + | 1.55006i | −0.224329 | + | 0.0601088i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −52.4012 | + | 30.2538i | −2.02898 | + | 1.17143i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.0410 | − | 27.7272i | 0.658842 | − | 1.07200i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.3535 | + | 28.3535i | −1.09457 | + | 1.09457i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9181 | + | 16.1185i | 1.07616 | + | 0.621323i | 0.929859 | − | 0.367917i | \(-0.119929\pi\) |
0.146304 | + | 0.989240i | \(0.453262\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.8309 | + | 24.5836i | 0.801780 | + | 0.946222i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 37.6671i | − | 1.44766i | −0.689977 | − | 0.723831i | \(-0.742379\pi\) | ||
0.689977 | − | 0.723831i | \(-0.257621\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.91507 | + | 6.78110i | −0.150247 | + | 0.260235i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.61111 | − | 0.872045i | 0.0617377 | − | 0.0334168i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.1988 | + | 11.8430i | 1.69122 | + | 0.453161i | 0.970705 | − | 0.240276i | \(-0.0772381\pi\) |
0.720517 | + | 0.693438i | \(0.243905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.5473 | − | 66.7659i | −1.47282 | − | 2.55100i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.402166 | − | 14.6303i | 0.0153436 | − | 0.558180i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.81766 | + | 24.8688i | 0.221635 | + | 0.947424i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.42504 | + | 27.7106i | 0.282462 | + | 1.05416i | 0.950674 | + | 0.310191i | \(0.100393\pi\) |
−0.668212 | + | 0.743971i | \(0.732940\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.24812 | + | 22.6853i | −0.0474120 | + | 0.861742i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.5753 | − | 61.8598i | 0.628736 | − | 2.34648i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50040 | + | 1.50040i | 0.0568318 | + | 0.0568318i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.74364 | + | 2.89874i | 0.103774 | + | 0.109641i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.75126 | −0.330531 | −0.165265 | − | 0.986249i | \(-0.552848\pi\) | ||||
−0.165265 | + | 0.986249i | \(0.552848\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.18736 | −0.233361 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.6158 | + | 15.4420i | 0.550462 | + | 0.581580i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.85100 | + | 9.85100i | 0.370485 | + | 0.370485i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.73251 | + | 25.1261i | −0.252845 | + | 0.943629i | 0.716432 | + | 0.697657i | \(0.245774\pi\) |
−0.969277 | + | 0.245972i | \(0.920893\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.93273 | + | 35.1285i | −0.0724829 | + | 1.31742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.98004 | − | 14.8537i | −0.149054 | − | 0.556275i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.6136 | − | 68.1323i | 0.770904 | − | 2.54800i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.000886156 | 0.0322372i | −3.30941e−5 | 0.00120392i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.9675 | − | 31.1206i | −0.670075 | − | 1.16060i | −0.977882 | − | 0.209155i | \(-0.932929\pi\) |
0.307807 | − | 0.951449i | \(-0.400405\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.86028 | − | 1.83821i | −0.255490 | − | 0.0684584i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.6057 | + | 13.8597i | −0.952288 | + | 0.515446i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.5979 | + | 42.6048i | −0.913544 | + | 1.58230i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.2791i | 1.08590i | 0.839764 | + | 0.542951i | \(0.182693\pi\) | ||||
−0.839764 | + | 0.542951i | \(0.817307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.43189 | − | 26.6338i | 0.164144 | − | 0.986436i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0578 | − | 10.4257i | −0.667892 | − | 0.385608i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.720934 | − | 0.720934i | 0.0266283 | − | 0.0266283i | −0.693667 | − | 0.720296i | \(-0.744006\pi\) |
0.720296 | + | 0.693667i | \(0.244006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.2441 | − | 26.4307i | 0.599172 | − | 0.974910i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.9118 | + | 25.3525i | −1.61751 | + | 0.933870i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.3751 | + | 6.53128i | −0.896652 | + | 0.240257i | −0.677578 | − | 0.735451i | \(-0.736970\pi\) |
−0.219074 | + | 0.975708i | \(0.570304\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.77823 | − | 6.50999i | −0.212269 | − | 0.239150i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.74994 | + | 0.736843i | −0.100885 | + | 0.0270321i | −0.308909 | − | 0.951092i | \(-0.599964\pi\) |
0.208023 | + | 0.978124i | \(0.433297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.7944 | − | 22.3980i | 1.42132 | − | 0.820598i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.28422 | + | 1.15028i | −0.0469872 | + | 0.0420865i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.42133 | − | 4.42133i | 0.161552 | − | 0.161552i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.7116 | + | 22.9275i | 1.44910 | + | 0.836636i | 0.998428 | − | 0.0560550i | \(-0.0178522\pi\) |
0.450669 | + | 0.892691i | \(0.351186\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.80257 | − | 22.8558i | 0.247899 | − | 0.832911i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.5538i | 1.51230i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.99976 | + | 17.3201i | −0.363448 | + | 0.629510i | −0.988526 | − | 0.151052i | \(-0.951734\pi\) |
0.625078 | + | 0.780562i | \(0.285067\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.0942 | + | 68.5316i | 1.34643 | + | 2.48754i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2935 | + | 3.29404i | 0.445640 | + | 0.119409i | 0.474659 | − | 0.880170i | \(-0.342571\pi\) |
−0.0290184 | + | 0.999579i | \(0.509238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.20983 | − | 2.09549i | −0.0437988 | − | 0.0758617i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.8488 | + | 6.50645i | 0.717635 | + | 0.235241i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.52798 | + | 0.176941i | 0.199604 | + | 0.00638897i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.98953 | + | 22.3532i | 0.215988 | + | 0.806078i | 0.985816 | + | 0.167827i | \(0.0536751\pi\) |
−0.769828 | + | 0.638251i | \(0.779658\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.6213 | + | 4.68365i | −0.706643 | + | 0.168677i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.75254 | − | 25.2008i | 0.242872 | − | 0.906410i | −0.731569 | − | 0.681767i | \(-0.761212\pi\) |
0.974441 | − | 0.224643i | \(-0.0721216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.84085 | − | 8.84085i | −0.317573 | − | 0.317573i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.16909 | + | 6.78549i | −0.257190 | + | 0.243428i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.42164 | 0.0509355 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.7136 | 0.991670 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40.5614 | − | 7.35388i | 1.44955 | − | 0.262806i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.75553 | + | 7.75553i | 0.276807 | + | 0.276807i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.78032 | − | 14.1083i | 0.134754 | − | 0.502908i | −0.865245 | − | 0.501349i | \(-0.832837\pi\) |
0.999999 | − | 0.00155884i | \(-0.000496195\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.88557 | − | 41.4138i | −0.351936 | − | 1.47437i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.23417 | − | 12.0701i | −0.114994 | − | 0.429163i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.7671 | − | 17.8760i | −0.595418 | − | 0.634795i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −41.0469 | − | 1.12832i | −1.45578 | − | 0.0400175i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.895558 | + | 1.55115i | 0.0317223 | + | 0.0549446i | 0.881451 | − | 0.472276i | \(-0.156567\pi\) |
−0.849728 | + | 0.527221i | \(0.823234\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.37058 | + | 1.97494i | 0.260752 | + | 0.0698683i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.9320 | − | 4.18247i | 0.704263 | − | 0.147780i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40.1255 | − | 69.4993i | 1.41600 | − | 2.45258i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.7717i | 1.15505i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.52702 | − | 1.04975i | −0.124157 | − | 0.0369528i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.09499 | + | 1.78689i | 0.108814 | + | 0.0628237i | 0.553419 | − | 0.832903i | \(-0.313323\pi\) |
−0.444605 | + | 0.895727i | \(0.646656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.8782 | + | 33.8782i | −1.18963 | + | 1.18963i | −0.212455 | + | 0.977171i | \(0.568146\pi\) |
−0.977171 | + | 0.212455i | \(0.931854\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.87193 | + | 2.37966i | 0.135794 | + | 0.0834582i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.1415 | − | 7.58724i | 0.460326 | − | 0.265769i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.4941 | + | 3.61574i | −0.472099 | + | 0.126499i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.8344 | − | 1.20609i | −0.483412 | − | 0.0421441i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.99495 | − | 2.14224i | 0.279026 | − | 0.0747647i | −0.116592 | − | 0.993180i | \(-0.537197\pi\) |
0.395618 | + | 0.918415i | \(0.370530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.3405 | + | 9.43421i | −0.569595 | + | 0.328856i | −0.756988 | − | 0.653429i | \(-0.773330\pi\) |
0.187393 | + | 0.982285i | \(0.439996\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 53.9787 | + | 33.1749i | 1.87930 | + | 1.15500i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.13655 | − | 4.13655i | 0.143842 | − | 0.143842i | −0.631519 | − | 0.775361i | \(-0.717568\pi\) |
0.775361 | + | 0.631519i | \(0.217568\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.3605 | + | 11.7551i | 0.707148 | + | 0.408272i | 0.810004 | − | 0.586424i | \(-0.199465\pi\) |
−0.102856 | + | 0.994696i | \(0.532798\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.7637 | − | 10.0491i | −1.17125 | − | 0.348599i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 11.1337i | − | 0.385761i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.0196 | − | 24.2827i | 0.485169 | − | 0.840338i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.862758 | + | 10.4409i | −0.0298213 | + | 0.360891i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.39163 | − | 1.71263i | −0.220664 | − | 0.0591266i | 0.146793 | − | 0.989167i | \(-0.453105\pi\) |
−0.367457 | + | 0.930041i | \(0.619771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.9686 | + | 29.3905i | 0.585124 | + | 1.01347i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 53.8070 | + | 1.47908i | 1.85321 | + | 0.0509423i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.2199 | + | 13.9254i | 1.41801 | + | 0.479049i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.90718 | + | 29.5100i | 0.271694 | + | 1.01398i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.997870 | − | 4.18039i | −0.0342468 | − | 0.143471i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.76290 | + | 32.7036i | −0.300388 | + | 1.12106i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.4996 | − | 19.4996i | −0.667652 | − | 0.667652i | 0.289520 | − | 0.957172i | \(-0.406504\pi\) |
−0.957172 | + | 0.289520i | \(0.906504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.4859 | − | 6.32097i | 0.427008 | − | 0.216173i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.2094 | 0.826978 | 0.413489 | − | 0.910509i | \(-0.364310\pi\) | ||||
0.413489 | + | 0.910509i | \(0.364310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.1352 | 1.43764 | 0.718818 | − | 0.695198i | \(-0.244683\pi\) | ||||
0.718818 | + | 0.695198i | \(0.244683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.64720 | − | 1.55907i | 0.0561366 | − | 0.0531329i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.6005 | − | 21.6005i | −0.735291 | − | 0.735291i | 0.236372 | − | 0.971663i | \(-0.424042\pi\) |
−0.971663 | + | 0.236372i | \(0.924042\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.8154 | + | 47.8277i | −0.435737 | + | 1.62619i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.3487 | + | 5.09600i | −0.725041 | + | 0.173069i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.9044 | + | 66.8200i | 0.607364 | + | 2.26671i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6295 | − | 27.3221i | −0.495703 | − | 0.925774i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.69938 | − | 17.3867i | 0.192895 | − | 0.588452i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.58061 | + | 4.46974i | 0.0872404 | + | 0.151105i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.03471 | − | 1.08110i | −0.136242 | − | 0.0365061i | 0.190053 | − | 0.981774i | \(-0.439134\pi\) |
−0.326296 | + | 0.945268i | \(0.605801\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.17196 | − | 9.55521i | −0.174446 | − | 0.322289i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.08884 | − | 8.81413i | 0.171447 | − | 0.296955i | −0.767479 | − | 0.641074i | \(-0.778489\pi\) |
0.938926 | + | 0.344119i | \(0.111822\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.9433i | 1.47881i | 0.673262 | + | 0.739404i | \(0.264893\pi\) | ||||
−0.673262 | + | 0.739404i | \(0.735107\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.53662 | + | 8.52273i | −0.0852675 | + | 0.286488i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.6015 | + | 11.3169i | 0.658153 | + | 0.379985i | 0.791573 | − | 0.611075i | \(-0.209263\pi\) |
−0.133420 | + | 0.991060i | \(0.542596\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.09062 | + | 4.09062i | −0.137195 | + | 0.137195i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.03192 | − | 52.4787i | −0.269079 | − | 1.75810i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.42746 | − | 2.55619i | 0.148159 | − | 0.0855398i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.93656 | − | 0.518898i | 0.0647319 | − | 0.0173449i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.5923 | + | 21.3213i | −1.42212 | + | 0.711897i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.4501 | + | 4.13985i | −0.515290 | + | 0.138072i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.7622 | + | 7.36828i | −0.425172 | + | 0.245473i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.6699 | + | 18.9880i | −0.388350 | + | 0.631882i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39.7714 | + | 39.7714i | −1.32205 | + | 1.32205i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.9105 | − | 13.2274i | −0.760732 | − | 0.439209i | 0.0688263 | − | 0.997629i | \(-0.478075\pi\) |
−0.829559 | + | 0.558420i | \(0.811408\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.2559 | − | 17.8013i | −0.904022 | − | 0.590431i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.39151i | 0.145497i | 0.997350 | + | 0.0727486i | \(0.0231771\pi\) | ||||
−0.997350 | + | 0.0727486i | \(0.976823\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.69500 | + | 2.93582i | −0.0560962 | + | 0.0971614i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34.6537 | − | 18.7571i | 1.14562 | − | 0.620090i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.74589 | − | 2.07551i | −0.255792 | − | 0.0685392i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.06543 | + | 12.2377i | 0.233067 | + | 0.403684i | 0.958709 | − | 0.284388i | \(-0.0917905\pi\) |
−0.725642 | + | 0.688072i | \(0.758457\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.228153 | − | 8.29991i | 0.00751790 | − | 0.273491i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.541920 | + | 16.9306i | −0.0178375 | + | 0.557279i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.12469 | + | 26.5897i | 0.234258 | + | 0.874264i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.5712 | + | 0.911726i | 0.544268 | + | 0.0299450i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.181846 | + | 0.678658i | −0.00596617 | + | 0.0222660i | −0.968845 | − | 0.247669i | \(-0.920336\pi\) |
0.962879 | + | 0.269935i | \(0.0870022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.27463 | − | 5.27463i | −0.172869 | − | 0.172869i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.8300 | + | 26.2337i | 0.812899 | + | 0.858853i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.0719 | 1.34319 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.7363 | 1.72282 | 0.861409 | − | 0.507912i | \(-0.169582\pi\) | ||||
0.861409 | + | 0.507912i | \(0.169582\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.2179 | + | 27.7000i | 0.855588 | + | 0.903955i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.4625 | − | 24.4625i | −0.797454 | − | 0.797454i | 0.185239 | − | 0.982693i | \(-0.440694\pi\) |
−0.982693 | + | 0.185239i | \(0.940694\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.01341 | − | 7.51413i | 0.0655655 | − | 0.244694i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.53493 | − | 21.0168i | 0.245111 | − | 0.683676i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.78982 | + | 36.5361i | 0.318126 | + | 1.18726i | 0.921043 | + | 0.389460i | \(0.127338\pi\) |
−0.602917 | + | 0.797804i | \(0.705995\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.6736 | + | 25.8723i | 1.35278 | + | 0.839849i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.835233 | − | 30.3847i | 0.0270843 | − | 0.985290i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.6532 | − | 23.6480i | −0.442271 | − | 0.766035i | 0.555587 | − | 0.831458i | \(-0.312494\pi\) |
−0.997858 | + | 0.0654232i | \(0.979160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.6443 | + | 4.19189i | 0.506239 | + | 0.135646i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 71.2833 | − | 38.5836i | 2.30426 | − | 1.24723i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.7867 | + | 25.6114i | −0.477489 | + | 0.827035i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.9349i | 0.868869i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.98957 | + | 12.2330i | −0.257460 | + | 0.394203i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.4217 | + | 14.6772i | 0.818355 | + | 0.472477i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.85578 | + | 8.85578i | −0.284783 | + | 0.284783i | −0.835013 | − | 0.550230i | \(-0.814540\pi\) |
0.550230 | + | 0.835013i | \(0.314540\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.62979 | − | 4.27892i | 0.0844811 | − | 0.137459i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.0062 | − | 19.6335i | 1.09131 | − | 0.630069i | 0.157386 | − | 0.987537i | \(-0.449693\pi\) |
0.933925 | + | 0.357468i | \(0.116360\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.7294 | + | 6.35828i | −0.760730 | + | 0.203837i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.3226 | + | 32.3277i | −0.682869 | + | 1.03531i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.3843 | + | 8.40939i | −1.00407 | + | 0.269040i | −0.723150 | − | 0.690691i | \(-0.757307\pi\) |
−0.280921 | + | 0.959731i | \(0.590640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.6806 | − | 20.0228i | 1.10840 | − | 0.639932i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.77239 | + | 4.21167i | 0.120443 | + | 0.134468i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.9552 | + | 23.9552i | −0.764054 | + | 0.764054i | −0.977052 | − | 0.212999i | \(-0.931677\pi\) |
0.212999 | + | 0.977052i | \(0.431677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59.5872 | − | 34.4027i | −1.89861 | − | 1.09616i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.32665 | − | 7.81724i | 0.0740580 | − | 0.248826i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 76.4446i | 2.43080i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.9059 | − | 31.0140i | 0.568801 | − | 0.985192i | −0.427884 | − | 0.903833i | \(-0.640741\pi\) |
0.996685 | − | 0.0813580i | \(-0.0259257\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.13649 | + | 16.8797i | 0.289938 | + | 0.535661i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.83658 | − | 1.29596i | −0.153330 | − | 0.0410846i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.138048 | − | 0.239107i | −0.00437204 | − | 0.00757259i | 0.863831 | − | 0.503782i | \(-0.168058\pi\) |
−0.868203 | + | 0.496209i | \(0.834725\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.1390 | − | 18.9583i | 0.415700 | − | 0.599815i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 624.2.cn.f.305.5 | 56 | ||
3.2 | odd | 2 | inner | 624.2.cn.f.305.14 | 56 | ||
4.3 | odd | 2 | 312.2.bp.a.305.10 | yes | 56 | ||
12.11 | even | 2 | 312.2.bp.a.305.1 | yes | 56 | ||
13.11 | odd | 12 | inner | 624.2.cn.f.401.14 | 56 | ||
39.11 | even | 12 | inner | 624.2.cn.f.401.5 | 56 | ||
52.11 | even | 12 | 312.2.bp.a.89.1 | ✓ | 56 | ||
156.11 | odd | 12 | 312.2.bp.a.89.10 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bp.a.89.1 | ✓ | 56 | 52.11 | even | 12 | ||
312.2.bp.a.89.10 | yes | 56 | 156.11 | odd | 12 | ||
312.2.bp.a.305.1 | yes | 56 | 12.11 | even | 2 | ||
312.2.bp.a.305.10 | yes | 56 | 4.3 | odd | 2 | ||
624.2.cn.f.305.5 | 56 | 1.1 | even | 1 | trivial | ||
624.2.cn.f.305.14 | 56 | 3.2 | odd | 2 | inner | ||
624.2.cn.f.401.5 | 56 | 39.11 | even | 12 | inner | ||
624.2.cn.f.401.14 | 56 | 13.11 | odd | 12 | inner |